We now turn our attention to the frequency response of the parallel
resonant bandpass filter (BPF)
circuit shown in Figure 
. Recall that a bandpass filter
passes frequencies between two limits. The range of frequencies between
the two limits is refered to as the passband
of the filter and the difference between the limiting frequencies as the
bandwidth 
of the filter.
Figure: Parallel Resonant Bandpass Filter Circuit
Figure: Frequency Response for a Parallel Resonant Bandpass Filter Circuit
The magnitude of the transfer function of this circuit is given by Equation
and the resonance frequency 
by Equation .
Resonance is a physical phenomenon in which stored energy oscillates between
two energy storage elements. In the BPF circuit shown in Figure ,
the magnetic energy stored in the inductor and the electric energy stored in
the capacitor are exchanged back and forth in harmony at resonance. Resonance
occurs at a single frequency 
determined by the values of L and C. The
frequency response magnitude attains a maximum at the resonant frequency.
A graph of the frequency response magnitude for the parallel resonant BPF is shown in
Figure .
using C = 47 nF and the estimated value of L for your
inductor found in Lab 5.
. Connect the function generator across the parallel
combination of the 47 nF capacitor and the inductor you made in Lab 5 (note that
you will have to do this twice, once for each student's inductor).
Reset the function generator by cycling the power. Set the amplitude (displayed)
to 1.0 
. Set the frequency to the values shown in Table and
record the AC voltage measured across the parallel combination of inductor and capacitor.
. Determine the inductance of your coil using this
frequency.
using LabVIEW.
, and the half power
frequencies 
and 
. Determine the bandwidth 
and the Q of the circuit given by Equation . Determine the inductance
of your coil using the resonance frequency found with LabVIEW.
Table: Bandpass filter experimental frequency response
